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Library Checkout Queue: M/M/c Queueing Simulator (2D)

A real queueing-theory model of a library's checkout desks: Poisson patron arrivals, exponential service times, live Erlang-C wait predictions and Little's Law readouts.

Education & Learning Tools2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

The 3D original renders a decorative library scene with no working formulas behind its sliders, so this 2D companion instead models the part of a library that genuinely runs on math: the checkout desk. Patrons arrive as a Poisson process at rate λ, each desk serves at rate μ with exponentially distributed service time, and the Erlang-C formula gives the theoretical average wait Wq alongside a running simulated average so you can watch the two converge as the queue plays out.

⚙ Under the hood

M/M/c queueing model: Poisson arrivals, exponential service, Erlang-C wait-time formula, and Little's Law (L = λ·W) relating queue length to wait time and arrival rate.

queueing theoryerlang cpoisson processlittle's lawm/m/c modeldiscrete event simulation

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install